Tory Eurosceptics have put on their biggest show of strength, rejecting pleas to show trust in the prime minister, with 114 Conservative MPs voting to regret the absence of an in-out referendum bill in the Queen's speech.

David Cameron's aides insisted the vote was not a blow to his authority, as he had given his backbenchers a free vote, but Cameron loyalists had pleaded with backbenchers to relent and trust the prime minister after he tried to placate them by rushing out a draft Conservative referendum bill.

Cameron has spent much of a three-day visit to the US battling to douse the Eurosceptic fires caused by the rise of Ukip.

Before the vote he maintained that he was extremely relaxed about how backbenchers voted and said nothing should be read into the outcome. But the previous largest Conservative show of sceptic strength had been in October 2011 when 81 MPs voted for a referendum.

Tory whips said they had not put any pressure on backbenchers, but many senior figures had taken to the airwaves urging restraint and trust in Cameron.

John Baron, leader of the Tory dissidents said: "We are going to keep at this. There is deep distrust out there. Legislation is more realistic than a manifesto promise."

The vote calling for regret over the Queen's speech was defeated by 277 to 130, including 11 Labour MPs and one Liberal Democrat.

Douglas Carswell, a leading sceptic, said the Conservative party would now unite behind a private members' bill offering a referendum, adding it could become law.

The result of a ballot for private member's bills will be announced today. Probably only the top seven MPs in the ballot have a chance of their bill being debated and becoming law, but William Hague, the foreign secretary, promised full Conservative support for the bill at a tough meeting of the backbench 22 committee.

Carswell said: "We have to realise we are no longer engaged in trench warfare, and fight a new much more mobile and flexible campaign. If we can get a majority in the Commons to give the bill a second reading, and that is a realistic prospect – there are many patriots on the Labour benches – that is a game changer. It will show for the first the Commons has a majority for an-in out referendum. That will give us momentum, and I have learnt in politics momentum is everything. The Tory party has to realise that Cameron is no longer the roadblock to a referendum, that it is Nick Clegg, and even he is already beginning to shift under pressure."

Carswell was referring to an earlier admission by the deputy prime minister that it was a matter of "when, rather than if", a referendum would be held. At prime minister's questions, Clegg said: "Just two years ago an absolute legal guarantee was given in legislation for the first time ever that when the [EU] rules change, there will be a referendum. I think it is a question of when, not if, because the rules are bound to change."

It is the most definitive Clegg has been that a referendum will be required owing to forthcoming EU reforms, and leaves Ed Miliband as the only leader saying a referendum is not inevitable.

The shadow chancellor, Ed Balls, said a commitment to a referendum now would be a massive gamble and a diversion from the economic crisis.

He claimed the Conservative party "has certainly been banging on about Europe day after day over the last week—banging the nails in the coffin of Tory modernisation and in the coffin of this prime minister's prime ministership".

But Clegg said his party would not let the Conservatives give government time to a private member's bill. He said: "The Conservative party are perfectly free for their own reasons to move the goalposts." But he added: "Legislation is already in place and the people of Britain have a guarantee about when a referendum will take place."

The business secretary, Vince Cable, speaking to businessmen in Birmingham on Wednesday night, accused Tories of risking the economy in response to the Ukip advance.

He said: "It is simply self-indulgent and reckless for parties or individuals to risk so much in order to address one concern raised in a council election by just 7% of the electorate." He said the Tories needed a reality check if they did not think the UK economy was dependent on the EU.

He added that Britain outside the EU means "an exodus of the non-EU firms headquartered in this country, precisely because they regard the UK as the gateway to Europe. The UK currently hosts more non-EU firms than Germany, France, Switzerland and the Netherlands combined, and remains the favourite destination for firms looking to establish a European HQ."

But Cameron in New York accused the Liberal Democrats and Labour of putting their heads in the sand. He said: "There are various responses you can make. You can make the response of sticking your head in the sand, pretending nothing has changed and just carrying on and accepting everything that comes out of Brussels. This is not a sensible approach although it does seem to be the approach that some in British politics seem to take."

The prime minister's remarks indicate that Clegg's change of tack over a referendum in the Commons appeared not to have gone far enough for No 10. Downing Street is mildly suspicious of Clegg's remarks because the prime minister's renegotiation would probably not trigger a referendum under the terms of the current legislation. This is because the prime minister is aiming to transfer sovereignty in the opposite direction – from Brussels back to the UK.

The prime minister said his three-pronged approach – reform, renegotiation and then a referendum by the end of 2017 – was right for Britain. He contrasted this with Labour and the Liberal Democrats.

"You have a very clear policy from the Conservatives. The focus should be on the other parties. Well what is your position? Are you going to trust the British people and allow them to have a say? We have a very very clear popular right position that is in the national interest and the other parties have now got to make their minds up."